Quantumness-generating capability of quantum dynamics

  • Nan LiEmail author
  • Shunlong Luo
  • Yuanyuan Mao


We study quantumness-generating capability of quantum dynamics, where quantumness refers to the noncommutativity between the initial state and the evolving state. In terms of the commutator of the square roots of the initial state and the evolving state, we define a measure to quantify the quantumness-generating capability of quantum dynamics with respect to initial states. Quantumness-generating capability is absent in classical dynamics and hence is a fundamental characteristic of quantum dynamics. For qubit systems, we present an analytical form for this measure, by virtue of which we analyze several prototypical dynamics such as unitary dynamics, phase damping dynamics, amplitude damping dynamics, and random unitary dynamics (Pauli channels). Necessary and sufficient conditions for the monotonicity of quantumness-generating capability are also identified. Finally, we compare these conditions for the monotonicity of quantumness-generating capability with those for various Markovianities and illustrate that quantumness-generating capability and quantum Markovianity are closely related, although they capture different aspects of quantum dynamics.


Quantum dynamics Quantumness Noncommutativity Quantum Markovianity 



This work was supported by the National Natural Science Foundation of China, Grant Nos. 11375259, 11405262, the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences, Grant No. Y029152K51, the Key Laboratory of Random Complex Structures and Data Science, Chinese Academy of Sciences, Grant No. 2008DP173182.


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Authors and Affiliations

  1. 1.RCSDS, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina

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